Method, system and medium for controlling manufacture process having multivariate input parameters
First Claim
1. A method for controlling a manufacturing apparatus, the method comprising the steps of:
- (a) identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;
(b) storing values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;
(c) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;
where;
i—
number of wafer;
k—
number of output;
yactual—
an empirical output value;
ypredicted—
a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}′
i) {right arrow over (X)}′
i=({right arrow over (X)}1′
i,X2′
i,X3′
i) is transformed input values in a vector format;
{right arrow over (X)}i=(X1i,X2i,X3i) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}; and
(d) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients.
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Abstract
A method, system, and medium of modeling and/or for controlling a manufacturing process is disclosed. In particular, a method according to embodiments of the present invention includes the step of identifying one or more input parameters. Each input parameter causes a change in at least two outputs. The method also includes the step of storing values of the identified inputs and corresponding empirical output values along with predicted output values. The predicted output values are calculated based on, in part, the values of the identified inputs. The method also includes the step of calculating a set of transform coefficients by minimizing a score equation that is a function of differences between one or more of the empirical output values and their corresponding predicted output values. The method further includes the steps of receiving a new set of values for the identified inputs, transforming the new set of values for the identified input using the set of coefficients, and calculating a set of predicted output values using the transformed input values.
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Citations
23 Claims
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1. A method for controlling a manufacturing apparatus, the method comprising the steps of:
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(a) identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;
(b) storing values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;
(c) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;
where;
i—
number of wafer;
k—
number of output;
yactual—
an empirical output value;
ypredicted—
a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}′
i){right arrow over (X)}′
i=({right arrow over (X)}1′
i,X2′
i,X3′
i) is transformed input values in a vector format;
{right arrow over (X)}i=(X1i,X2i,X3i) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}; and
(d) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (2, 3)
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4. A system for controlling a manufacturing apparatus, the system comprising:
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(a) means for identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;
(b) a memory device configured to store values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;
(c) means for calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;
where;
i—
number of wafer;
k—
number of output;
yactual—
an empirical output value;
ypredicted—
a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}′
i){right arrow over (X)}′
i=(X1′
i,X2′
i,X3′
i) is transformed input values in a vector format;
{right arrow over (X)}i=(X1i,X2i,X3i) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}; and
(d) means for calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (5, 6)
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7. A computer readable medium for storing instructions being executed by one or more computers, the instructions directing the one or more computers for predicting output characteristics of a device produced by a manufacturing apparatus, the instructions comprising implementation of the steps of:
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(a) identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;
(b) storing values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;
(c) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;
where;
i—
number of wafer;
k—
number of output;
yactual—
an empirical output value;
ypredicted—
a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}′
i){right arrow over (X)}′
i=(X1′
i,X2′
i,X3′
i) is transformed input values in a vector format;
{right arrow over (X)}i=(X1i,X2i,X3i) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}; and
(d) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (8, 9)
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10. A method for controlling a manufacturing apparatus, the method comprising the steps of:
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(a) identifying at least one input that causes a change in at least two of a plurality of outputs;
(b) storing values of the identified inputs and corresponding empirical output values;
(c) calculating and storing predicted output values, based on, in part, the values of the identified inputs;
(d) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values; and
(e) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (11, 12, 13, 14)
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15. A system for controlling a manufacturing apparatus, the system comprising:
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(a) means for identifying at least one input that causes a change in at least two of a plurality of outputs;
(b) a memory device configured to store values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;
(c) means for calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values; and
(d) means for calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (16, 17, 18, 19)
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20. A computer readable medium for storing instructions being executed by one or more computers, the instructions directing the one or more computers for predicting output characteristics of a device produced by a manufacturing apparatus, the instructions comprising implementation of the steps of:
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(a) identifying at least one input that causes a change in at least two of a plurality of outputs;
(b) storing values of the identified inputs and corresponding empirical output values;
(c) calculating and storing predicted output values, based on, in part, the values of the identified inputs;
(d) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values; and
(e) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients. - View Dependent Claims (21, 22, 23)
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Specification